This thread was a blast to read. Who sez theory ain't fun? Way too much thinking going on on this one fella's. Look-it, it would have helped to know the rest of the progression. Better yet, just telling us the key signature would have cut this thread in have (except for maybe "Equators" ramblings), but my guess is the proper root for this chord is the G# or Ab if you prefer, making the chord just a simple G# add4
The break down is as follows:
Root = G#
3rd = C
Perfect 4th = C#
Perfect 5th = D#